Lobatto IIIA-IIIB discretization of the strongly coupled nonlinear Schrödinger equation

Authors:
A. Aydın;B. Karasözen
Affiliations:
Department of Mathematics, Atılım University, 06836, Ankara, Turkey;Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, 06531, Ankara, Turkey
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

In this paper, we construct a second order semi-explicit multi-symplectic integrator for the strongly coupled nonlinear Schrodinger equation based on the two-stage Lobatto IIIA-IIIB partitioned Runge-Kutta method. Numerical results for different solitary wave solutions including elastic and inelastic collisions, fusion of two solitons and with periodic solutions confirm the excellent long time behavior of the multi-symplectic integrator by preserving global energy, momentum and mass.